532 Pages
    by Chapman & Hall

    The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and other applications.

    The authors focus on examining the way a response variable depends on a combination of explanatory variables, treatment, and classification variables. They give particular emphasis to the important case where the dependence occurs through some unknown, linear combination of the explanatory variables.

    The Second Edition includes topics added to the core of the first edition, including conditional and marginal likelihood methods, estimating equations, and models for dispersion effects and components of dispersion. The discussion of other topics-log-linear and related models, log odds-ratio regression models, multinomial response models, inverse linear and related models, quasi-likelihood functions, and model checking-was expanded and incorporates significant revisions.

    Comprehension of the material requires simply a knowledge of matrix theory and the basic ideas of probability theory, but for the most part, the book is self-contained. Therefore, with its worked examples, plentiful exercises, and topics of direct use to researchers in many disciplines, Generalized Linear Models serves as ideal text, self-study guide, and reference.

    The Origins of Generalized Linear Models
    Scope of the Rest of the Book
    An Outline of Generalized Linear Models
    Processes in Model Fitting
    The Components of a Generalized Linear Model
    Measuring the goodness of Fit
    An Algorithm for Fitting Generalized Linear Models
    Models for Continuous Data with Constant Variance
    Error Structure
    Systematic Component (Linear Predictor)
    Model Formulae for Linear Predictors
    Tables as Data
    Algorithms for Least Squares
    Selection of Covariates
    Binary Data
    Binomial Distribution
    Models for Binary Responses
    Likelihood functions for Binary Data
    Models for Polytomous Data
    Measurement scales
    The Multinomical Distribution
    Likelihood Functions
    Log-Linear Models
    Likelihood Functions
    Log-Linear Models and Multinomial Response Models
    Multiple responses
    Conditional Likelihoods
    Marginal and conditional Likelihoods
    Hypergeometric Distributions
    Some Applications Involving Binary data
    Some Aplications Involving Polytomous Data
    Models with Constant Coefficient of Variation
    The Gamma Distribution
    Models with Gamma-distributed Observations
    Quasi-Likelihood Functions
    Independent Observations
    Dependent Observations
    Optimal Estimating Functions
    Optimality Criteria
    Extended Quasi-Likelihood
    Joint Modelling of Mean and Dispersion
    Model Specification
    Interaction between Mean and Dispersion Effects
    Extended Quasi-Likelihood as a Criterion
    Adjustments of the Estimating Equations
    Joint Optimum Estimating Equations
    Example: The Production of Leaf-Springs for Trucks
    Models with Additional Non-Linear Parameters
    Parameters in the Variance function
    Parameters in the Link Function
    Nonlinear Parameters in the Covariates
    Model Checking
    Techniqes in Model Checking
    Score Tests for Extra Parameters
    Smoothing as an Aid to Informal Checks
    The Raw Materials of Model Checking
    Checks for systematic Departure from Model
    Check for isolated Departures from the Model
    A Strategy for Model Checking?
    Models for Survival Data
    Proportional-Hazards Models
    Estimation with a Specified Survival distribution
    Example: Remission Times for Leukemia
    Cox's Proportional-Hazards Model
    Components of Dispersion
    Linear Models
    Nonlinear Models
    Parameter Estimation
    Example: A Salamander mating Experiment
    Further Topics
    Bias Adjustment
    Computation of Bartlett Adjustments
    Generalized Additive Models
    Elementary Likelihood Theory
    Edgeworth Series
    Likelihood-Ratio Statistics
    Index of Data Sets
    Author Index
    Subject Index
    Each chapter also contains Bibliographic Notes and Exercises


    P. McCullagh

    "... an important, useful book, well-written by two authorities in the field..."
    -Times Higher Education Supplement
    "... an enormous range of work is covered... represents, perhaps, the most important field of research in theoretical and practical statistics. For all statisticians working in this field, the book is essential."
    -Short Book Reviews
    "... this is a rich book; rich in theory, rich in examples, and rich in a statistical sense. I highly recommend it."
    "... a definitive and unified presentation...by the outstanding experts of this field."
    "This is a wonderful book... Reading the book is like listening to a good lecturer. The authors present the material clearly, and they treat the reader with respect. There is a balance between discussion, mathematical presentation of models, and examples."

    "... a complete introduction to the topic in a single monograph... a very readable book that provides the reader with great insight into a vast array of data analysis techniques...
    -Siam Review

    "... a unique and useful text for intermediate undergraduate teaching."